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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Mathematical analysis detailing the effect of leakage in hydraulic tappets.

Identifier  ExFiles\Box 17\6\  Scan289
Date  24th July 1934
  
To E.{Mr Elliott - Chief Engineer}
to By.{R.W. Bailey - Chief Engineer}

X7060

Hs{Lord Ernest Hives - Chair}/Smth.3/KW.24.7.34.

Effect of Leakage in Hydraulic Tappets.

Let L = load on rocker end.
k = mechanical advantage of system (i.e. movement of 1 unit of plunger causes movement of k units at rocker end).
d = diameter of plunger.
b = length of plunger.
c = clearance between plunger and casing.

---

Then oil pressure under the plunger
= total pressure / area ∝ kL / d²

For oil of given viscosity, rate of leakage may be taken as proportional to
((clearance)² x oil pressure x circumference of plunger) / (length of plunger)

i.e. ∝ (c² kL x d) / (d² x b) ∝ c² KL / db{Donald Bastow - Suspensions}

Travel of plunger due to this leakage
∝ Total leakage / area ∝ c²kL / d³b

Travel at rocker end
∝ travel of plunger x k ∝ c²k²L / d³b
  
  


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